Discovery and Analysis of Lightweight S-Boxes Using Memetic Algorithms

Abstract

UNIVERSITY OF NEW ENGLAND Abstract Computational Science School of Science & Technology Doctor of Philosophy Discovery and Analysis of Lightweight S-Boxes Using Memetic Algorithms by Meaad TORI This thesis addresses the challenge of discovering and designing critical components within lightweight cryptographic primitives to enhance security against advanced cryptographic attacks. Emphasising the significant role of S-Boxes in symmetric cryptography, the research investigates optimised design and integration strategies to elevate both security and efficiency within constrained environments. Through a detailed examination of cryptographic systems, cryptanalysis strategies, and studying many lightweight cryptographic algorithms, this work lays a foundation for understanding the needs to enhance the security and efficiency in lightweight cryptographic environments. The core investigation focuses on utilising evolutionary algorithms, specifically memetic and genetic search algorithms, to discover and optimise Substitution Boxes (S-Boxes). To validate our approach, we replicated a study that introduced the concept of "Golden S-Boxes", which exhibit superior properties essential for robust cryptographic functions. This thesis demonstrates how these evolutionary algorithms navigate extensive search spaces to discover S-Boxes that meet stringent security requirements with efficient performance which can then be integrated into lightweight cryptographic systems. Our approach successfully replicated the discovery of 4x4 Golden S-Boxes, and we enhance the algorithm to support all S-Box sizes. Our code provides specific properties selected to find candidate S-Boxes that balance between security considerations and suitability for use in lightweight environments. While our code currently considers only linear equivalent S-Boxes, it can be updated to include other variations. Additionally, our code is open-source, allowing for further customisation and improvement by the community. Although we do not offer customisable properties based on size, the code can be adjusted to generate S-Boxes of any size, and users can add or omit properties and fine-tune parameters as needed. For instance, we present a 5x5 candidate S-Box, similar in size and properties to the one used in the ASCON cryptographic standard. The approach in this research apply both the theory and practice of lightweight cryptographic methods. The methods developed offer a scalable way to enhance cryptographic strength, showing clear improvements in security and efficiency for modern applications, particularly in lightweight environments.